One of the most interesting results is to find that a consistent description of all the experimental results on particle ratios obtained from the lowest AGS to the highest ALICE Heavy Ion Collider energies is possible within the framework of a thermal statistical model.We pursue our investigation of the validity of our quantum mechanically correlated statistical correction (IHRG) inspired by a Beth-Uhlenbeck corrected form of the equation of state (EoS) to the ideal hadron resonance gas model (HRG). We calculate the ratios of some particle yields of equal masses, namely (p/p,K − /K + ,π − /π + , Λ/Λ, Σ/Σ, Ω/Ω), and some particle yield with unequal masses, namely (p/π + , k + /π + ,k − /π − , Λ/π − ,p/π − , Ω/π − ). We then study the center-of-mass energy variation of these ratios of particle yields obtained by our new corrected hadron resonance gas model (IHRG). Our model results are then confronted with the corresponding calculations obtained using the ideal hadron resonance gas (HRG) model, the Cosmic Ray Monte Carlo (CRMC) EPOS 1.99 simulations, as well as the experimental data from AGS, SPS, RHIC, and ALICE. Our new (IHRG) model results generally show very close agreement with the experimental data compared with the other models considered. Especially remarkable is the very good matching obtained for our new IHRG model with the pair p/π − and p/π + , which suggests that our new model IHRG might be helpful in describing the famous proton anomaly at top RHIC and LHC energies. However, in some cases of unequal mass and (multi)strange content, like Λ/π − , and Ω/π − , appear to be quite large and thus alert further investigations on the suitability of thermal hadron gas models and their need for further modification.